THERE is an old picture of Chvrches where they're under a neon sign that promises: There Will Be No Miracles Here.

You have to wonder though.

The Glasgow electro icons have dedicated the last five years to conquering continents, roaring their gospel – a rapturous, enlightening doctrine that draws on industrial synth-pop, feminist punk, epic post-rock, dance-floor anthems and immaculate R&B. Their home-recorded second album, Every Open Eye, tore up charts across the world when it was released last autumn (Top 10 in the US, Top Five in the UK, Number One in Scotland); its 2013 predecessor, The Bones Of What You Believe, is edging toward one million sales; and they headline Glasgow enormodome SSE Hydro next weekend – despite having only played around 10 shows in Scotland to date.

Such achievements are extraordinary, if not miraculous, as is their knack for concurrently coming across as stadium-filling international pop stars and a well-loved local indie act. It's a brilliant trick of the light, or quantum physics, or black magic, or – most likely – ingenious cyber nous. And it's crucial to Chvrches' exceptional charms. They're a grassroots band with global reach.

All of which means that they're rarely back in their home-town, let alone all at once. And so it is that vocalist Lauren Mayberry takes time out to talk on the phone during a week's holiday in New York, while her synth-brandishing colleagues Martin Doherty and Iain Cook suggest an interview in a Glasgow pub that spirals into nigh-on eight hours and covers – among other marvels – Wasabi Kit-Kats, reggae, typography; their alleged alignment with cryptic cult The Illuminati; sportswear, capes and Quincy Jones; and whether Lionel Blair invented the pas-de-basque.

Heavy metal looms large, too. “I feel like we've spent most of this interview talking about Iron Maiden,” muses Cook about three hours in, and flaunts the band's cut-throat commercial instinct by shifting the conversation not to Chvrches' latest single or tour, but rather to his bygone Christian rock troupe, Ephis Dammim. “It's Hebrew for boundaries of blood,” he says, as a scarlet votive is placed on our table.

“The candle of shame,” says Doherty, shaking his head. “Day turns to night.”

“It's night-time now,” Cook declares, in what feels like a Kelvinbridge out-take from The Lost Boys. “More drinks?”

In the beginning, there were Chvrches: a secret cabal who were born on the internet. There were few clues in the early days as to the trio's Scottish indie lineage (Blue Sky Archives, Aereogramme, The Unwinding Hours, Julia Thirteen, The Twilight Sad); there was simply a thrilling synth-dirge, Lies (2012), anonymously dispatched online. It exploded, spectacularly, everywhere at once – Europe, America, Asia, Australia. Its title resonated across The Bones of What You Believe, then rebounded in the opening salvo of Every Open Eye – “Throw me no bones, and I will tell you no lies, this time...”

If their debut was fixated on anatomy (Lungs, By The Throat) and hidden depths (We Sink, Under The Tide), then Every Open Eye feels more outward-looking, and landscape-focused (perfect storms and turning tides; myriad references to leaving traces, drawing lines in the sand, and burying entities – memories? Bones?). There is a sense of distance. Perhaps of letting go.

Taking a step back was crucial for their second album, says Mayberry, down a long line from America. “Having the space to figure out what we wanted to do this time was really important,” she offers. “Part of that, for me, was finding an aspect of the band that felt more comfortable, because although I'm really proud of what we achieved with the first album, it did all feel like a bit of a sh**storm,” she says with a laugh. “I was pretty exhausted from feeling I was fighting my corner all the time” – Mayberry's righteous take-downs of online misogynists have been well-documented – “and I wanted to find a better more positive way to frame things.

“I wanted to put a bit more distance between the real life and the band versions of me,” she continues. “But I also started thinking – what is it I actually like about being in a band? What is it I like about writing? And I think it's about communication, at the end of the day.” This ethos is echoed in Chvrches' Fanclvb community, and in Mayberry's feminist collective, TYCI.

Like the band themselves, Every Open Eye has a knack for feeling intimate yet universal; for appearing near and faraway at once. (Much of the album chimes with Rebecca Solnit's meditation on loss and landscape, A Field Guide To Getting Lost – specifically, her chapters on The Blue of Distance.) But, says Mayberry, there was no over-arching theme for the record.

“I got to the point of over-analysis – I got caught up in wondering what I wanted the lyrical themes on the record to be – but I never approach writing like that. Ever.” She offers. “In the end, I wrote Never Ending Circles in about 45 minutes on a train – it was just a rough stream-of-consciousness thing. Taking a step back like that ended up being the way I wrote lyrically for this record, and that all started with Never Ending Circles.”

Light years (well, three thousand miles) back in Glasgow, talk revolves round that cardinal song – which opens Every Open Eye – as the candle burns. “It was really important to us to try and capture the same dynamic we had on album one with this record,” says Doherty. “Same studio [Alucard, in Cook's spare room], us producing, same set up. Day one, we all went in, and just like that: Never Ending Circles.”

Cook elaborates. “Day one, Martin walks straight up to one of our new synths and goes – [mimics the album's ripping, rippling opening hook]. I was like that – 'Martin, that is absolute sh**e,'” he laughs. “I came round to it eventually.”

Doherty grins. “I was trying to write the world's most annoying riff.”

Cook: “It worked.”

There's a meticulous (but never cold) precision to Every Open Eye – a hi-octane minimalism that evokes the ultra-pop productions of Quincy Jones. There's plenty space, but it's never empty. “We were obsessed with that on this record,” nods Doherty. “We were constantly like – 'Can we take anything else out? Are there any elements that are working against the DNA or the economy of the song?' We thought we could do a lot more with less this time,” he says. “Sounds and ideas have to stand up for themselves if they're more exposed.”

Bang in the middle of the record, there's a euphoric, melancholic anthem called Clearest Blue, whose lyrics give the album its title. It's bold and bright and exquisite. “Clearest Blue was one of those moments in the studio where you get that flash of light,” offers Cook. “You can see the crowd, you can see how it's going to pan out. You don't get many of those moments in a career, let alone on an album.”

Doherty had a similar revelation as Clearest Blue materialised. “To go from that first day of playing it and jumping around the studio, to seeing 10 thousand people bouncing at the same time to that song at [London's] Alexandra Palace – that's serious,” he says. “That's amazing.”

Chvrches have long induced such fevered communal exultation. As with their debut, Every Open Eye plays out as two perfectly-crafted sides of vinyl – and simultaneously as a glorious 11-track club set. “It was sequenced for vinyl, but I love the club thing, although I hadn't thought of it before,” says Cook. “I also read that someone's done a blog about how the album follows the dramatic arc of a John Hughes movie. Maybe there's something universal about that narrative form.”

It's a formidable illusion though, conjuring so many distinct narratives in parallel. How do they do it? “I'll tell you how you do it,” Doherty deadpans. “Eighty or 100 revisions of a tracklist.”

Cook buries his head in his hands.

“Oh well,” Doherty brightens. “On album three, we can relax a bit. We can do whatever we want.”

Cook nods. “I might even be willing to relax my 45 minute rule on album three. The double album rule still stands though. No double albums.”

“What about the no shorts on stage rule?” Doherty ventures.

Cook looks through him. “Come on, man. That stays”.

Given their escalating banks of synths, how about capes, a la Rick Wakeman?

“Capes are fine,” shrugs Cook. “I love capes. Wizard hats, that's cool. But sportswear? Not good.”

Chvrches wear their fortunes lightly. They bear the weight of their pop miracles well.

Chvrches play Glasgow SSE Hydro (with support from The Twilight Sad) on April 2.